In mathematics (also in physics and neighbouring disciplines) a theorem is sometimes said to be folklore when the community feels that it has been around and generally accepted as true for a long time, without however a proof of it having been submitted and published in the usual manner.

The sociology of folklore theorems can be subtle. In semi-formalized areas such as theoretical physics folklore convictions, correct ones and incorrect ones, have seriously impeded progress.

folklore, $[\ldots]$ is a technical term for a method of publication in category theory. It means that someone sketched it on the back of an envelope, mimeographed it (whatever that means) and showed it to three people in a seminar in Chicago in 1973, except that the only evidence that we have of these events is a comment that was overheard in another seminar at Columbia in 1976. Nevertheless, if some younger person is so presumptuous as to write out a proper proof and attempt to publish it, they will get shot down in flames. – Paul Taylor, blog comment (2012)